U(1) problem on a lattice. II. Strong-coupling expansion

We calculate the mass difference between the π and η mesons in lattice QCD with Wilson fermions using the strong-coupling expansion. We obtain the result that the mass difference first appears at the order of (1/$g^2$N${)}^6$ in the ordinary phase where the parity and flavor symmetry are conserved and that $m_{\pi }$(π meson mass)$m_{\eta }$(η meson mass) and ${\lim }_{{\mathrm{m}}_{\mathrm{\pi }}\to 0}$ ${\mathrm{m}}_{\mathrm{\eta }}$≠0. Furthermore, we point out that the dynamics which makes the η meson heavier than the π meson leads to the spontaneous parity and flavor-symmetry breaking (〈ψ¯i${\gamma }_5$ ${\tau }^3$ψ〉≠0) for $M_0$ ${\mathrm{}}^2$$M_c$${\mathrm{}}^2$=4 [or $K^2$>$K_c$ ${\mathrm{}}^2$=(1/4), where the hopping parameter K=1/(2$M_0$)].